The sum of three consecutive numbers is 54. Taking the middle number a

1.	The sum of three consecutive numbers is 54. Taking the middle number as x, find:(i) expression for the smallest number and the largest number.(ii) the three numbers.
Answer» Sum of three consecutive numbers = 54 Middle number = x (i) The first number = x – 1 and third number = x + 1 (ii) ∴ x + x-1+x+1 = 54 ⇒ 3x = 54 ⇒ x= 54/3 = 18 ∴ First number =18-1 = 17 and third number =18 + 1 = 19 ∴ Three required numbers are 17, 18,19

The sum of three consecutive numbers is 54. Taking the middle number as x, find:(i) expression for the smallest number and the largest number.(ii) the three numbers.

Answer»

Sum of three consecutive numbers = 54

Middle number = x

(i) The first number = x – 1

and third number = x + 1

(ii) ∴ x + x-1+x+1 = 54

⇒ 3x = 54

⇒ x= 54/3 = 18

∴ First number =18-1 = 17

and third number =18 + 1 = 19

∴ Three required numbers are 17, 18,19